A variety of models have been proposed for the production of precursors to
compact binary mergers. These include explosive fireball models
[1]}, gamma-ray flares
[2]}, [3]}, shock-powered radio precursors
[4]}, unipolar inductors [5]}, [6]},
crustal shattering [2]}. Particular examples of
reconnection-based models include Refs.
[8]}, [9]} , where dissipation in (transient) current sheets powers the emission. Especially the latter class of models requires a non-linear
interaction of magnetic fields in reconnecting current sheet, whose
boundary conditions are determined by the global dynamics of the problem
[10]}. This motivates the need for global numerical
simulations of the magnetospheric dynamics in a close compact binary. To
study the precursor emission mechanism numerically different types of
simulations have been performed. In particular, simulations in
special-relativistic force-free electrodynamics have clarified the emission
of single orbiting neutron stars [11]}, idealized
mixed binaries [12]}, and magnetospheric interaction in
binary neutron star systems [8]}. Studies in dynamical
spacetimes have focused on understanding electromagnetic bursts produced
from single neutron stars, either in isolation [14]}, or
as mimickers for post-merger remnants [15]}. A small number
of studies has also focused on the magnetospheric dynamics
during the collapse
[16]}, [17]}, [18]} and collision of
neutron stars [19]}, where their
magnetospheres were inactive. Full general-relativistic simulations of
force-free electrodynamics have been conducted to better understand the
common magnetosphere prior to merger, see, e.g., for black hole binaries
[20]}, [21]}, [22]}, [23]},
neutron star binaries
[24]}, [25]}, [26]}, and mixed
systems [27]}, [28]}. While several numerical
formulations of relativistic force-free electrodynamics have been proposed
(e.g.,
[29]}, [30]}, [14]}, [32]}, [33]}, [34]}, [35]}),
most of the simulations mentioned above have used a variation of
independently evolving electric and magnetic fields according to the
relativistic Maxwell equations [36]}, [14]}. The
latter is supplemented by a suitable prescription for the electric current
mimicking a (resistive) force-free pair plasma  (see,
e.g., Refs. [38]}, [39]}, [40]} for
a recent discussion).
